Numerical Analysis of Markov-Perfect Equilibria with Multiple Stable Steady States: A Duopoly Application with Innovative Firms

21 Pages Posted: 10 Mar 2016

See all articles by Herbert Dawid

Herbert Dawid

Bielefeld University - Department of Business Administration and Economics; Center for Mathematical Economics

Michel Keoula

Bielefeld University - Department of Business Administration and Economics

Peter M. Kort

Tilburg University - Department of Econometrics & Operations Research; Tilburg University - Center for Economic Research (CentER)

Date Written: March 1, 2016

Abstract

This paper presents a numerical method for the characterization of Markov-perfect equilibria of symmetric differential games exhibiting coexisting stable steady-states. The method relying on the calculation of 'local value functions' through collocation in overlapping parts of the state space, is applicable for games with multiple state variables. It is applied to analyze a piecewise deterministic game capturing the dynamic competition between two oligopolistic firms, which are active in an established market and invest in R&D. Both R&D investment and an evolving public knowledge stock positively influence a breakthrough probability, where the breakthrough generates the option to introduce an innovative product on the market. Additionally, firms engage in activities influencing the appeal of the established and new product to consumers. Markov-perfect equilibrium profiles are numerically determined for different parameter settings and it is shown that for certain constellations the new product is introduced with probability one if the initial strength of the established market is below a threshold, which depends on the initial level of public knowledge. In case the initial strength of the established market is above this threshold, the R&D effort of both firms quickly goes to zero and with a high probability the new product is never introduced. Furthermore, it is shown that after the introduction of the new product the innovator engages in activities weakining the established market, although it is still producing positive quantities of that product.

Keywords: Markov-Perfect Equilibrium, Skiba Curve, Collocation, R&D Competition, Product Innovation

Suggested Citation

Dawid, Herbert and Keoula, Michel and Kort, Peter, Numerical Analysis of Markov-Perfect Equilibria with Multiple Stable Steady States: A Duopoly Application with Innovative Firms (March 1, 2016). Bielefeld Working Papers in Economics and Management No. 05-2016. Available at SSRN: https://ssrn.com/abstract=2745762 or http://dx.doi.org/10.2139/ssrn.2745762

Herbert Dawid (Contact Author)

Bielefeld University - Department of Business Administration and Economics ( email )

P.O. Box 100131
D-33501 Bielefeld, NRW 33501
Germany
+49-521-1064843 (Phone)
+49-521-1062994 (Fax)

Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Michel Keoula

Bielefeld University - Department of Business Administration and Economics ( email )

P.O. Box 100131
D-33501 Bielefeld, NRW 33501
Germany

Peter Kort

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands
+31 13 466 2062 (Phone)
+31 13 466 3072 (Fax)

HOME PAGE: http://center.uvt.nl/staff/kort/

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 2062 (Phone)
+31 13 466 3072 (Fax)

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